Probability Lesson 6.2.1.

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2 Probability 6.2.1 California Standard: What it means for you:Lesson6.2.1ProbabilityCalifornia Standard:Statistics, Data Analysis, and Probability 3.3Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1–P is the probability of an event not occurring.What it means for you:You’ll learn about using probability as a way to describe how likely events are to happen.Key words:probabilitychancelikelypercentfractiondecimal

3 What are the chances that I will roll a six?Lesson6.2.1ProbabilityA lot of the time, you can’t say for sure whether or not one particular event will happen. But you can often say how good the chances are.What are the chances that I will roll a six?Probability is a way of using numbers to describe the chance of an event happening.

4 Probability 6.2.1 Some Events Are More Likely to Happen Than OthersLesson6.2.1ProbabilitySome Events Are More Likely to Happen Than OthersPeople often talk about things that might happen, using words like “chance,” “likely,” and “probability”:“What is the probability it will snow today?”“How likely is it that the school football team will win its next game?”“What is the chance that you will go to a movie this weekend?”Look at the line below and think about where your answer would be for each of these questions.ImpossibleVery unlikelyFairly unlikelyEven chanceQuite likelyVery likelyCertain

5 Probability 6.2.1 Guided PracticeLesson6.2.1ProbabilityGuided PracticeDecide where you would put the chances of the following events happening on this scale:ImpossibleVery unlikelyFairly unlikelyEven chanceQuite likelyVery likelyCertain1. Leaves falling from the trees next fall.2. Finding a live elephant in your bedroom when you get home.3. Winning a raffle if you have 1 out of 100 tickets.CertainVery very unlikelyVery unlikelySolution follows…

6 6.2.1 Probability Probability Guided PracticeLesson6.2.1ProbabilityProbabilityGuided PracticeDecide where you would put the chances of the following events happening on this scale:ImpossibleVery unlikelyFairly unlikelyEven chanceQuite likelyVery likelyCertain4. Winning a raffle if you have 99 out of 100 tickets.5. Winning a raffle if you have 1 out of 1,000,000 tickets.6. A tossed coin landing on heads.Very likelyVery very unlikelyEven chanceSolution follows…

7 Probability 6.2.1 Guided PracticeLesson6.2.1ProbabilityGuided Practice7. Put the events named in Exercises 1–6 in order, from most likely to least likely.Leaves falling from the trees next fall.Finding a live elephant in your bedroom when you get home.Winning a raffle if you have 1 out of 100 tickets.Winning a raffle if you have 99 out of 100 tickets.Winning a raffle if you have 1 out of 1,000,000 tickets.A tossed coin landing on heads.Most likely146352Least likelySolution follows…

8 Probability 6.2.1 Probability Is a Way to Say How Likely an Event IsLesson6.2.1ProbabilityProbability Is a Way to Say How Likely an Event IsIn math, probability is a way of describing the chance that an event will occur. Probability can be written using fractions, decimals, or percents.You can replace the words on the line below with numbers that represent how likely an event is to occur:ImpossibleVery unlikelyFairly unlikelyEven chanceQuite likelyVery likelyCertain0 or 0%1 or 100%or 50%12

9 Lesson6.2.1Probability0%50%100%12A probability of 0 (or 0%) means that there is no chance.A probability of 1 (or 100%) means that the event will definitely happen.A probability of (or 50%) means that the eventmight happen, but there’s an equal chance that it won’t.12

10 Probability 6.2.1 Guided PracticeLesson6.2.1ProbabilityGuided PracticeEstimate the probability that each of the following things will happen. Write your answers as percents.8. It will go dark tonight.9. Your math teacher will turn into a pineapple.10. A 6th-grader from California chosen at random will be a girl.100%0%About 50%Solution follows…

11 Probability 6.2.1 Guided PracticeLesson6.2.1ProbabilityGuided PracticeUse the list of probabilities below to answer Exercises 11–12.1258251011. Which of the probabilities above represents an impossible event?12. Which of the probabilities above represents a certain event?2510Solution follows…

12 Probability 6.2.1 Probability Is Usually Calculated ExactlyLesson6.2.1ProbabilityProbability Is Usually Calculated ExactlyThere are many situations where you can say exactly what the probability of an event is.This isn’t the same as saying whether an event will definitely (or not definitely) happen — it’s just a measure of how likely the event is.

13 Lesson6.2.1ProbabilityExample 1What is the probability of spinning the color red on this spinner?What is the probability of spinning the color blue?SolutionSpinning the color red is certain, so the probability is 1.Spinning the color blue is impossible, so the probability is 0.Solution follows…

14 Lesson6.2.1ProbabilityExample 2What is the probability of spinning the color blue on this spinner?SolutionThe blue section is one-fourth of the spinner.So the probability of spinning the color blue is= 0.25 = 25%14If you spun the spinner lots of times, about one-fourth of the spins would land on blue.Solution follows…

15 Probability 6.2.1 Guided PracticeLesson6.2.1ProbabilityGuided PracticeExercises 13–15 are about this spinner.Find the probability of spinning the colors below.Write your answers as decimals.13. Blue14. Yellow15. PinkHalf the spinner is blue, so the probability of spinning blue is one-half or 0.5.Half the spinner is yellow, so the probability of spinning yellow is one-half or 0.5.It is impossible to spin pink, so the probability is 0.Solution follows…

16 Probability 6.2.1 Guided PracticeLesson6.2.1ProbabilityGuided PracticeIn Exercises 16–18, find the probability of spinning the color yellow on each of the following spinners.Write your answers as fractions.16.17.18.141315Solution follows…

17 Probability 6.2.1 Independent PracticeLesson6.2.1ProbabilityIndependent PracticeEach set of cards shown below is turned over and shuffled, then one card is picked.A.B.C.D.A:B:C:D:1. a triangle card2. a star cardFor each set of cards, find the probability of picking:14151514251Solution follows…

18 Probability 6.2.1 Independent PracticeLesson6.2.1ProbabilityIndependent PracticeA bag has 1 red, 1 blue, and 2 yellow marbles in it.3. How many marbles are in the bag?4. How many marbles are red? What is the probability of drawing a red marble?5. How many marbles are blue? What is the probability of drawing a blue marble?6. How many marbles are yellow? What is the probability of drawing a yellow marble?4114114212Solution follows…

19 Probability 6.2.1 Independent PracticeLesson6.2.1ProbabilityIndependent Practice7. The probability of an event occurring is Which two values below represent this same probability?380.375375%0.375%37.5%38%8. The probability of an event occurring is 55%. Which two values below represent this same probability?0.55100551001120555.5Solution follows…

20 Probability 6.2.1 Independent PracticeLesson6.2.1ProbabilityIndependent Practice9. In a tiled hallway, kids are jumping from one tile to the next. The probability of landing on a green tile is 60%.What fraction of the hallway area is covered with green tiles?35Solution follows…

21 Lesson6.2.1ProbabilityRound UpProbability is useful because you can use it to compare the chances of different events happening.The event with the highest probability is the most likely to occur.